Problem: Simplify the following expression: $a = \dfrac{-2k^2 - 18k - 28}{k + 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ a =\dfrac{-2(k^2 + 9k + 14)}{k + 7} $ Then we factor the remaining polynomial: $k^2 + {9}k + {14} $ ${7} + {2} = {9}$ ${7} \times {2} = {14}$ $ (k + {7}) (k + {2}) $ This gives us a factored expression: $\dfrac{-2(k + {7}) (k + {2})}{k + 7}$ We can divide the numerator and denominator by $(k - 7)$ on condition that $k \neq -7$ Therefore $a = -2(k + 2); k \neq -7$